Consider the following game: your friend has two urns with 10 balls each. She picks a ball from the first urn and shows the number on it (call it f ) to you. Then you guess Larger or Smaller and she picks a new ball from the second urn. If the new ball's number's (s ) greatness is guessed correctly with respect to the first ball then you get $s , if they are equal you get , otherwise you get nothing. What is the maximum expected return of this game?